Why was ELIZA able to induce "delusional thinking"?
I like your choice of "induce" instead of "produce," because the delusions came from the users. This means the answer has to do mostly with human psychology; people come equipped with lots of mental machinery specialized for dealing with other humans and not very much mental machinery specialized for dealing with software. So ELIZA behaved in ways that some people classified it as a person and behaved accordingly, and others didn't.

What features will trip up a person's internal person classification system seem like they vary heavily from person to person, and also with experience and familiarity. Going into more detail is, as mentioned in the comments, more appropriate for sites specializing on the human side of the keyboard.